As stated by the European League Against Rheumatism (EULAR) and the Société Française de Rhumatologie (SFR), treatment of patients with rheumatoid arthritis (RA) should target sustained remission or at least low disease activity. However, despite significant advances based on various combinations of conventional synthetic disease-modifying antirheumatic drugs (DMARDs) and biologic DMARDs, RA therapies meet treatment goals only in some patients: * 40 to 50% of patients with early RA, treated with methotrexate (MTX) monotherapy as first-line therapy, * 20 to 30% of patients treated with a combination of MTX and biologic as second-line therapy. * Less than 10% of patients treated with a combination of MTX and another targeted DMARD, such as baricitinib, as third-line therapy. Therefore, new strategies targeted at achieving a higher percentage of remission are needed, that do not require waiting for multiple failed therapies. Combinations of biologics have shown synergistic improvement of symptoms in murine models of RA relative to the improvement observed with either agent alone. However, in RA patients, only five randomised clinical trials (RCTs) have explored the efficacy and safety of combining tumour necrosis factor (TNF) inhibitor with another biologic (anakinra, abatacept, rituximab or bimekizumab). Baricitinib is a selective, reversible and competitive inhibitor of Janus kinases (Jaki). This treatment is efficient in a number of therapeutic scenarios in RA and showed a clinical superiority over adalimumab in one RCT (RA-BEAM study in MTX inadequate responders). Of note, baricitinib inhibits many of the pro-inflammatory cytokines involved in the pathogenesis of RA but does not block signalling downstream of TNF. Owing to the interest in combining different mechanisms of action, the investigators plan to assess the efficacy and safety of combination therapy with baricitinib and a TNF inhibitor. The investigators are aware that combining targeted therapies is not recommended due to a potential increase in the frequency of serious adverse events. However, several case series on patients treated with a combination of targeted therapies have been published, suggesting a certain efficacy in patients with refractory RA. The first ones focused on inflammatory bowel diseases and psoriasis, but more recently, combination of tofacitinib (which belongs to the same Jaki family as baricitinib) with various biologics has been reported in a sample of RA patients. No serious adverse effects were reported over a mean of approximately 11 months of therapy. The clinical improvement was mild but noticeable in these refractory RA cases. Recently, data of interest from the RA-BEAM study have been reported. Patients who switched from adalimumab to baricitinib showed improvements in disease control. Because the switch from adalimumab to baricitinib occurred without a washout period, and because adalimumab has a mean circulating half-life of approximately 14 days, patients would have received several weeks of dual TNF and Jak1/Jak2 inhibition in the course of the change of treatment. The observation of increased efficacy, with no apparent acute safety issues during the weeks when patients were exposed to both adalimumab and baricitinib, is of interest, and supports our strategy to combine the two treatments for patients with refractory RA. The investigators consider that there is a need for investigation into the addition of anti-TNF to baricitinib in patients suffering of refractory RA (inadequate response to TNF inhibitors). The investigators hypothesize that in this population, based on ACR50 score, this combination therapy will decrease disease activity more efficiently than a switch to another targeted DMARD, such as baricitinib.